The peak of Mount Everest is about 9,000 feet higher than the top of Mt. McKinley. I think your comment about the "tallest mountain" is right, though (in terms of the vertical distance from base to peak) -- it's just that Mt. Everest is probably on a much higher plateau than 3,000 feet.
On another note, Canada's Mount Logan may be the most massive mountain in the world. It's peak is only 19,550 feet above sea level, but the mountain covers an enormous area -- in fact, there is no real "peak" in a true sense -- the summit is a ridge that is more than ten miles long.
Last week Jay Leno had a bunch of Jaywalking finalists on his show. When he asked what was the highest point on earth, one contestant suggested "Mars." When Jay indicated that wasn't right, she changed her guess to "Pluto."
Mt. McKinnley is 20,320' above sea level. Everest is almost 9000' higher. That said, besides spelling and addition errors, if you want to get finnicky, the mountain in Hawaii is the highest, rising up from the seabed.
That said, Denali (Mt McKinnley) is the harder of those to climb. Because Denali is in the Arctic Circle, the weather is always terrible. I know....I've attempted Denali thrice and failed thrice. Perhaps next Spring...